Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Corollary 6.3.7.5. Let $S$ be a simplicial set. Then the composite morphism

\[ \operatorname{N}_{\bullet }( \operatorname{{\bf \Delta }}_{S} ) \xrightarrow { \psi _{S} } \operatorname{Sd}(S) \xrightarrow { \lambda _{S} } S \]

is universally localizing.

Proof. By virtue of Proposition 6.3.6.10, this follows from the observation that the morphisms $\lambda _{S}$ and $\psi _{S}$ are universally localizing (Proposition 6.3.7.2 and Variant 6.3.7.4). $\square$